Control of an NV center as a two-qubit system
Résumé
Nitrogen-vacancy (NV) centers are promising experimental platforms for quantum information processing. In this paper, we investigate their controllability and fundamental quantum speed limit for two-qubit gates. Such a quantum system consists of two coupled spins, an electronic and a nuclear spin, where only the former can be controlled directly via microwave pulses. We discuss the various physical approximations that lead to the system model before studying its controllability. We use this control issue as an example to demonstrate how standard geometric control tools can be applied to spin networks. We complete this analysis with a computation of the quantum speed limit using known analytical techniques on Lie groups and their algebras. We finally demonstrate, thanks to preliminary optimal control numerical experiments, that this limit can be approached while keeping a reasonable energy of the control field.
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